A new vertex selection scheme for polygon-based contour coding is proposed. The proposed method consists of 'two-step procedure'. Initial vertices are selected by using the conventional iterated refinement method (IRM) or progressive vertex selection (PVS) method. A vertex adjustment process then follows where the initial vertices are updated to produce an optimal polygon in the sense of 'error area'. In this step, the geometrical information of the partial contour and its polygon segment is used to reduce the search region for the admissible vertex position. Experimental results are presented to compare the approximation performances and the required computational burdens of the proposed and conventional methods.